Yet what else would you call a dog that can directly convey her wants and needs?

Sofia is able to express — with a keyboard symbol system that announces each word when pressed — her various urges. There’s a symbol for walk, food, play and toy. If she’s thirsty, she’ll often lick her lips, pant and race to the water symbol.

Sofia has learned how to use each symbol in the correct context and never uses it when out of earshot of her owner.

Does Sofia have the capacity for abstract thought and reasoning? And if Sofia can do it, does it mean yours can, too?

in “The Genius of Dogs,” husband and wife team Brian Hare and Vanessa Woods, both research scientists, present the case that dogs are far savvier than we ever thought, based on years of research that Hare conducted at Duke University’s Canine Cognition Center.

Dogs might not be as objectively smart as primates, but our four-legged friends actually surpass monkeys (and other intelligent beasts) in communication skill and relationship with humans, the book argues.

In fact, “Dogs had independently evolved to be cognitively more similar to us than we were to our closest relatives [primates] . . . Dogs are geniuses in their ability to read our gestures. Their skills are similar to what we observe in infants.”

That’s right, your dog — Spot who sniffs crotches and Rex who chases its tail — is a mastermind.

The book takes on the notion that dogs have been dumbed down through years of domestication. Hare argues that wolves, which dogs began evolving from between 12,000 and 40,000 years ago, are better at certain things (like hunting, for example) than dogs, but pups surpass wolves at many communication tests.

Pointing gestures provide some of the most fruitful evidence for dogs’ unique intelligence — and they fare better at it than both wolves and primates.

Puppies as young as six weeks can spontaneously discern human gestures. And it doesn’t matter how much time a puppy spends with humans, their pointing instinct seems instead to be ingrained. For example, shelter dogs are just as good as family-raised dogs at figuring out pointing gestures.

But pointing is the just the tip of the iceberg. Take Chaser, a border collie, who is often called “the world’s smartest dog.” Chaser has learned the names of more than 1,000 objects. And her ability to learn new words has not decreased the more that she has learned. In addition, Chaser is able to distinguish between categories. She knows which of these objects are “toys” and “non-toys,” and also which ones are “balls” or “Frisbees.”

In other test with different subjects, dogs were successful in bringing back a certain toy after having been shown a replica of the toy (a hot-dog toy, for example). In the same test, a small percentage of the dogs could actually return the correct toy after only being showed a picture of it.

Not only do they seem to understand abstractions, they also seem to make expectations about the world around them.

When a dog is played a recording of its owner’s voice and then showed a picture of a stranger, the dogs often looked at the picture longer “as if [he was] surprised” by the mismatch.

“They could only form such an expectation if — when they hear their owner’s voice — they also remember what their owner looks like. The dogs could be doing this only by making an inference,” the book says.

The powers of inference and communicative intelligence sometimes makes for craftier canines.

When dogs observed humans interacting with other humans or dogs, they often would pick out the “better” partner. In one case, the human shared food with another human, while another person stole food from the other person. In another, the human played tug of war with the dog and let the dog win, in the other, the human won. In both situations, the dog preferred the more generous human.

“Dogs seemed skilled at detecting which individuals will be the best cooperative partners,” Hare says.

Dogs also are adept at making life easier. Experimenters tested the ability of dogs to make shortcuts. First, the experimenter showed the dog where he hid the food. Then the dog was blindfolded, its ears plugged, and its scent blunted. The experimenter then walked the dog 30 meters away from the food, then pivoted 90 degrees, and headed 10 meters in another direction.

“In 97% of trials, the dogs found the food in just over 20 seconds on average. This means dogs can solve third-grade trigonometry —they take the hypotenuse of the triangle, the shortest distance between their location and the reward,” the book says.

Our hairy Einsteins might be able solve trig problems and remember thousands of words — but dognition has its limits. Remember Sofia, the keyboard-pressing doggy genius?

When her owner introduced her to the family’s new pet, a guinea pig, Sofia did not run to the “play” symbol.